This invention relates generally to optical pattern recognition, and more particularly to the computation of image moments for object identification.
Image moments have been used for some time in the field of pattern recognition. In a visual image, let f(x,y) be a measure of brightness at the point (x,y). The geometric moments of the image are defined by ##EQU1## where x.sup.m y.sup.n is the generating function of the geometric moments, m, n=0, 1, 2, . . . and integration is over the entire visual image. Brightness can be regarded as analogous to mass. .mu..sub.00 is the total brightness or mass of the image, .mu..sub.20 and .mu..sub.02 can be thought of as moments of inertia of the image about the y and x axes, and so forth. Given an input image, one can evaluate a chosen set of its moments.
An advantage of applying pattern recognition techniques to these moments rather than directly to the image is that the number of the moments required to recognize the object may be less than the total number of elements in the image.
In applying pattern recognition techniques to image moments, a small number of moments are computed for an isolated object and these moments or combinations thereof are used to determine the object from a small library of objects of interest and their appropriate moments. These calculations are normally done on a digital computer as described, for example, in the article "Aircraft Identification by Moment Invariants", by S. A. Dudani et al. IEEE Transaction on Computers, Vol. C-26, No. 1 (1977) pp. 39-45.
Digital techniques for computing image moments are as accurate as the data input and the simple moments can be calculated for imagery being acquired at the rate of 30 frames per second or possibly greater. The digital equipment required, however, is complex, bulky and expensive. In addition, complex moments may not be calculable in real time. Optical techniques for calculating the simple moments have been proposed but are complicated in the case of the proposal of M. R. Teague in "Optical Calculations of Irradiance Moments", Applied Optics 19, pp. 1353-1356 (1980), or limited to simple geometric moments in the proposal of D. Casasent and D. Psaltis in "Hybrid Processor to Compute Invariant Moments for Pattern Recognition", Optics Letters 5, pp. 395-397 (1980). An earlier proposal by the latter authors in "Optical Pattern Recognition Using Normalized Invariant Moments", Proceedings of the Soc. of Photo-Optical Instrumentation Engineers, Vol. 201, pp. 107-114 (1979) had additional limitations in that it computed only one moment at a time and the moments had a bias which had to be considered and which further limited the dynamic range.